Using the variational discretization concept proposed in [1]}, we
consider the following temporally discrete problem:
\(\min \limits _{U \in U_{\text{ad}}}J_{\alpha ,\tau }(U) := \frac{1}{2} \Vert {(\mathcal {S}_{\alpha ,\tau }\mathcal {R}_{\theta _0} U)(T-) - y_d} \Vert _Y^2 + \frac{\nu }{2} \Vert {U} \Vert _{L^2(0,T;Z)}^2.\) 
